ELI5: Explain Like I'm 5

Moment-generating function

A moment-generating function is like a calculator. It is used to calculate the mean, variance, and other measures of a group of numbers. It takes in a list of numbers and spits out the answers to your questions about that group of numbers. For example, if you want to know the average of a group of numbers, you can use the moment-generating function to quickly figure it out.